( 693 ) 
so that we can really represent F(x) as the sum of n series of 
polynomials. We shall arrive at 
bnl FUE) 0) 
phan 
k=0 ki 
nou} VAN k=n—1 F (in+k) (0 
= — | (m—1),_ a(a—1)ft& TE ak iced (1X) 
m=1 am hl k=0 (An + k)! 
which result may also be written as follows: 
h=n—1 _ FH) (O 
ES —— ee © 
ni h! 
m=0 | h=mnatn—1 . FW (0) [=] 
> = (ml) ———— gh (a—1) : 
m=1 a” =n hy 4 h! 
a] 
. Ln denn 
The sien | indicates here the integers of h:n. 
n 
The region of divergence G2 of this series consists of the complex 
of the images of the circle unity in the u-plane made with the aid 
of the successive equations 
pi Creel es Ay, 
a—u 
and for the convergence in a point z it is necessary that the condition 
| en Ayn | a Aj” 
| | a—l } a—l 
is satisfied. 
Fig. 5. 
For a definite singular point A; on account of this inequality z 
